An athletic club for boys and girls has 375 members. There are 23 more boys than girls. How many of each are there?

Let's denote the number of girls in the athletic club as \( g \) and the number of boys as \( b \). We are given two pieces of information: 1. The total number of members in the club is 375, so we have the equation: \( g + b = 375 \). 2. There are 23 more boys than girls, so we have the equation: \( b = g + 23 \). We can now solve this system of equations to find the number of girls and boys in the athletic club. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}g+b=375\\b=g+23\end{array}\right.\) - step1: Substitute the value of \(b:\) \(g+g+23=375\) - step2: Add the terms: \(2g+23=375\) - step3: Move the constant to the right side: \(2g=375-23\) - step4: Subtract the numbers: \(2g=352\) - step5: Divide both sides: \(\frac{2g}{2}=\frac{352}{2}\) - step6: Divide the numbers: \(g=176\) - step7: Substitute the value of \(g:\) \(b=176+23\) - step8: Simplify: \(b=199\) - step9: Calculate: \(\left\{ \begin{array}{l}b=199\\g=176\end{array}\right.\) - step10: Check the solution: \(\left\{ \begin{array}{l}b=199\\g=176\end{array}\right.\) - step11: Rewrite: \(\left(b,g\right) = \left(199,176\right)\) The solution to the system of equations is \( b = 199 \) and \( g = 176 \). Therefore, there are 199 boys and 176 girls in the athletic club.